{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "349e0b4e",
   "metadata": {},
   "source": [
    "# Закон больших чисел"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f169da4",
   "metadata": {},
   "source": [
    "Закон больших чисел (ЗБЧ) в теории вероятностей — принцип, описывающий результат выполнения одного и того же эксперимента много раз. Согласно закону, среднее значение конечной выборки из фиксированного распределения близко к математическому ожиданию этого распределения.\n",
    "\n",
    "1. Построить пару примеров из реальной жизни\n",
    "2. Слабый закон и усиленный закон, чем отличаются"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27e92d89",
   "metadata": {},
   "source": [
    "### Игральная кость "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b14e8e53",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "441d0c89",
   "metadata": {},
   "source": [
    "Функция для генерации случайных величин от 1 до 6, словно число на верхней грани упавшей игральной кости"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "71f91a4a",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [1, 2, 3, 4, 5, 6] # случайные величины\n",
    "\n",
    "def roll_dice():\n",
    "    return random.choice(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "69bb5641",
   "metadata": {},
   "outputs": [],
   "source": [
    "results = [] # случайные величины\n",
    "cumulative_sum = [] # средние значения случайной величины\n",
    "num_rolls = 1_000 # количество подбрасываний игральной кости\n",
    "current_sum = 0 # переменная для хранения текущей суммы результатов подбрасываний"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "31bb3a98",
   "metadata": {},
   "outputs": [],
   "source": [
    "# подбрасываем кость num_rolls раз и записываем результаты в список\n",
    "for i in range(1, num_rolls + 1):\n",
    "    number = roll_dice()\n",
    "    current_sum += number\n",
    "    \n",
    "    results.append(number)\n",
    "    cumulative_sum.append(current_sum / i)\n",
    "\n",
    "# вычисляем среднее значение результатов подбрасываний\n",
    "mean = current_sum / len(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71dbabc5",
   "metadata": {},
   "source": [
    "Математическое ожидание дискретной случайной величины - это сумма произведений случайных величин на их вероятность. \n",
    "\n",
    "Для игральной кости распределение случайных величин равномерное:\n",
    "\n",
    "| i индекс               |  0  |  1  |  2  |  3  |  4  |  5  |\n",
    "| ---------------------- | --- | --- | --- | --- | --- | --- |\n",
    "| Xi случайная величина  |  1  |  2  |  3  |  4  |  5  |  6  |\n",
    "| Pi вероятность         | 1/6 | 1/6 | 1/6 | 1/6 | 1/6 | 1/6 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2d810e10",
   "metadata": {},
   "outputs": [],
   "source": [
    "P = [1 / len(X)] * len(X)\n",
    "M = sum(x * y for x, y in zip(X, P))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7e6e749b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Математическое ожидание:  3.5\n",
      "Среднее значение:  3.513\n",
      "Разница с мат. ожиданием:  -0.0129999999999999\n"
     ]
    }
   ],
   "source": [
    "print(\"Математическое ожидание: \", M)\n",
    "print(\"Среднее значение: \", mean)\n",
    "print(\"Разница с мат. ожиданием: \", M - mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17d5cc99",
   "metadata": {},
   "source": [
    "Строим график и видим как среднее значение случайных величин стримится к мат. ожиданию"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d5d5738c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(cumulative_sum)\n",
    "plt.axhline(y = mean, color = 'r', linestyle = '-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de0b35b0",
   "metadata": {},
   "source": [
    "<strong>Отличие ЗБЧ от усиленного ЗБЧ</strong> - усиленный закон задает более сильное утверждение, что среднее значение этой последовательности стремится к математическому ожиданию сходится <i>почти наверное</i>"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Edit Metadata",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
